I want to run a scenario where a hidden sniper is attacking the PCs.

1) Is such a scene structurally shown in any of the books?

2) How would the structure look like? I mean does the sniper roll for stealth first to hide, then start initiative rolls? For each PC action I guess they would have to roll perception vs. stealth to find him first, then next action they get shoot the sniper (assuming the sniper doesn't move again and try hiding again). It seems to me, that the sniper would get the first initiative slot automatically if he won the stealth roll before the initiative roll, because the PCs won't know to do anything till he strikes.

I just do it all with initiative. Sniper rolls his simple Cool check. PCs roll a Vigilance check with whatever you deem appropriate for a Difficulty. Some use the Sniper's Stealth dice pool to set the Difficulty. I'm ok with just using range and then upgrading and adding Setbacks as appropriate for conditions.

It means the sniper will likely go first, but a real Peter Parker character who has invested in their initiative skills might spot them.

Point being the PCs are likely to 'lose' the roll, and the sniper will go first, and they will be behind the power curve in the encounter, which is pretty much how it should be when someone starts shooting at you from who the F knows where.

I've also incorporated if the PCs actually can 'succeed' on their initiative roll, even if the sniper is going first, they spot their location. Anyone else has to make a Perception check to do so.

I don't like having a bunch of pre-initiative rolls, it just makes it all feel clunky to me.

A quality sniper is likely to be well outside normal Perception check range, so like the pirate says, I'd handle it with normal initiative and maybe give the sniper some Boost dice for concealment, range, etc - likely based on a Stealth check. I might even consider throwing some Setback on PC initiative checks.

In the past, I allowed the sniper to get one shot off (which missed) before we rolled initiative, but in retrospect I think my efforts to deploy a surprise overrode RAW and player agency. I think just saying, "okay, everyone make a Vigilance-based initiative check!" is probably just as much a surprise as a free combat round, and if a PC happens to go first, I'm not going to say anything about why they're in structured time. Why would a PC have the ability to sense an incoming ambush from a sniper over a klick away? Only the Force knows for sure.

My version was to on the initiative roll have the targets use Vigilance vs. the sniper's Stealth, while the sniper uses straight Cool.

Once started the sniper would (assuming you're doing it stereotypical) start the encounter with full concealment (AoR 228) unless he didn't hide or the players used a triumph or something.

I tried the whole "must succeed a perception check first" thing a couple times, but it wasn't so fun because if the players had poor perception or bad rolls the sniper could do huge amounts of damage before the players could even return fire.

11 hours ago, Darth Poopdeck said:

It seems to me, that the sniper would get the first initiative slot automatically if he won the stealth roll before the initiative roll, because the PCs won't know to do anything till he strikes.

10 hours ago, themensch said:

In the past, I allowed the sniper to get one shot off (which missed) before we rolled initiative, but in retrospect I think my efforts to deploy a surprise overrode RAW and player agency . I think just saying, "okay, everyone make a Vigilance-based initiative check!" is probably just as much a surprise as a free combat round, and if a PC happens to go first, I'm not going to say anything about why they're in structured time.

Emphasis mine. Lot's of players in my group, including me, have wanted to play or played stealthy characters and looked for rules for surprise and surprise rounds. They aren't there, you just roll Vigilance if you are surprised, no matter how stealthy the attack is. Fortunately, themensch and Ghostofman (apropos of nothing, what a nice ironic pairing of names), have already given some good ideas, but I'll elaborate. I would definitely give the sniper's Cool check several boost dice and almost certainly give the PC's Vigilance some setback, mitigated by how alert they are. This last part is important for you: If you don't give them some time before the encounter to role-play their level of alertness, they may be upset at all the setback dice, but if you gave them plenty of time to look around and they don't, they will usually be okay with the setback. If there is a sniper in the group or someone else who likes to fight at longer ranges, you could casually suggest that the abandoned buildings over there/tree-lined ridge/mountain cave/ com tower would be a great sniper nest. You would be surprised how often PC's miss really obvious clues like that (I still do). There is no arguing over setback after that.

Rolling Vigilance vs. the sniper's stealth is a brilliant idea. I don't think it's strictly RAW, but it's not outside the rules either. It might be a little too brutal, though. Before reading that I had thought of giving your sniper a homebrew version of Adversary, where he upgraded opponent's Initiative checks (since Initiative checks are usually Simple, the first level of Sniper Adversary would add one purple die to the pc's Initiative rolls, the next would change the die to red, etc). Still, Ghostofman's idea is good, if you want your PC's to have virtually no chance of going first.

So far, everyone seems to be in agreement that even if your PC's win Initiative, they should have no idea where the sniper is or possibly why they are even in structured time. I agree with this. I think the sniper needs a weapon that can fire at Extreme range, although you may have him fire closer if that suits the story, but the ability to fire from nearly anywhere will give this nemesis (It is a nemesis, right?) excellent flexibility. Most of the sniper weapons in this game are Slow-Firing 1 and I would absolutely keep that for a sniper encounter. It ratchets up the tension (When is he going to fire? Why didn't he fire? Did he move? Where is he?), gives your PC's a short break from an extremely lethal weapon that they probably don't have the ability to fight back against yet, and the sniper can use the off-round to change location and aim.

For a more in-depth encounter, I would try to give the PC's more to do than just make Perception checks until they find the sniper. A formidable Ranged (Heavy) check might be able to identify the caliber of the weapon, the range the shooter fired from, or even the identity of the weapon; decrease the difficulty by one for each shot the sniper has fired. Survival or Streetwise checks might be able to pick out likely spots for a sniper's nest, depending on if they are in a mainly urban setting or a mainly rural one. The appropriate Knowledge skill might suffice for either of those checks, too. You might ask for Discipline or Cool checks if the pc's go a couple rounds without spotting the sniper or if someone is hit. If you make the terrain an interesting tumble of different elevations and broken trees/rocks/duracrete (think of bombed-out Dresden, or Sarajevo, or Mogadishu, or Aleppo), you can ask for Athletics and Coordination checks.

Sometimes snipers mine and bomb the areas around them to provide extra protection. Throw in some hidden explosives if you think it won't overwhelm your PC's. Then they will be looking for bombs, not just the sniper, and will have to use Mechanics to diffuse them (or collect them if they are resourceful). You can also use this to hint to your PC's that they are getting close to the sniper's location. The newest supplement, No Disintegrations, has some new talents under Martial Artist that let the attacker pick their Critical instead of rolling, with some game-balancing restrictions. If you have access to this information, you could crib these talents (Precision Strike, Improved Precision Strike, Supreme Precision Strike) for NPC use: if your sniper aims at a particular body part and rolls a Critical, you might pick a particular Critical related to that area of the body, with some self-imposed restrictions. It is a pretty common and vicious tactic for snipers to maim the first target while he is out in the open, leaving him exposed, screaming, and unable to move. Then they pick off anyone who runs out of cover to try and rescue the first target.

Sniper encounters are best used with friendly npcs. The enemy slots one to start, the the players make their initiative rolls.

And if you truly want to GM on the dark side, that one shot that killed an npc is all they make. The sniper bugs out afterward, having completed the job they were hired for.